The present invention relates to ellipsometry and polarimetry, and more particularly comprises quasi-achromatic multi-element lens(es) and the application thereof in focusing, and optionally re-colliminating), a spectroscopic electromagnetic beam into a very small, chromatically relatively undispersed, area spot on a material system, said achromatic multi-element lens(es) providing relatively constant focal length at each wavelength in a large range of wavelengths, including into the deep UV; and said present invention is further a method for breaking correlation between, and evaluating parameters in parameterized equations for calculating retardance entered to, or between, orthogonal components in a beam of spectroscopic electromagnetic radiation by quasi-achromatic multi-element input and/or output optical elements, (eg. lens(es)), and a typically ellipsometrically indistinguishable, adjacently located, investigated material system with which the spectroscopic beam of electromagnetic radiation is caused to interact.
The practice of ellipsometry is well established as a non-destructive approach to determining characteristics of material systems, and can be applied in real time process control. The topic is generally well described in a number of publication, one such publication being a review paper by Collins, titled xe2x80x9cAutomatic Rotating Element Ellipsometers: Calibration, Operation and Real-Time Applicationsxe2x80x9d, Rev. Sci. Instrum, 61(8) (1990).
In general, modern practice of ellipsometry typically involves causing a spectroscopic beam of electromagnetic radiation, in an imposed, known, state of polarization, to interact with a material system at one or more angle(s) of incidence with respect to a normal to a surface thereof, in a plane of incidence. (Note, a plane of incidence contains both a normal to a surface of an investigated material system and the locus of said beam of electromagnetic radiation). Changes in the polarization state of said beam of electromagnetic radiation which occur as a result of said interaction with said material system are indicative of the structure and composition of said material system. The practice of ellipsometry utilizes said changes in polarization state by proposing a mathematical model of the ellipsometer system and the material system investigated by use thereof, obtaining experimental data by application of the ellipsometer system, and applying square error reducing mathematical regression, (typically), to the end that parameters in the mathematical model which characterize the material system are evaluated so that the obtained experimental data, and values calculated by use of the mathematical model have a xe2x80x9cbest matchxe2x80x9d relationship.
A typical goal in ellipsometry is to obtain, for each wavelength in, and angle of incidence of said beam of electromagnetic radiation caused to interact with a material system, material system characterizing PSI and DELTA values, (where PSI is related to a change in a ratio of magnitudes of orthogonal components rp/rs in said beam of electromagnetic radiation, and wherein DELTA is related to a phase shift entered between said orthogonal components rp and rs, caused by interaction with said material system;             PSI      =              "LeftBracketingBar"                              r            p                    /                      r            s                          "RightBracketingBar"              ;    and        DELTA    =                  (                              ∠            ⁢                          xe2x80x83                        ⁢                          r              p                                -                      ∠            ⁢                          xe2x80x83                        ⁢                          r              s                                      )            .      
As alluded to, the practice of ellipsometry requires that a mathematical model be derived and provided for a material system and for the ellipsometer system being applied. In that light it must be appreciated that an ellipsometer system which is applied to investigate a material system is, generally, sequentially comprised of:
a. a Source of a beam electromagnetic radiation;
b. a Polarizer element;
c. optionally a compensator element;
d. (additional element(s) such as lens(es), beam directing means, and/or windows such as in vacuum chambers);
e. a material system;
f. (additional element(s) such as lens(es), beam directing means, and/or windows such as in vacuum chambers);
g. optionally a compensator element;
h. an Analyzer element; and
i. a Detector System.
Each of said components b.-i. must be accurately represented by a mathematical model of the ellipsometer system along with a vector which represents a beam of electromagnetic radiation provided from said source of a beam electromagnetic radiation, Identified in a. above)
Various ellipsometer configurations provide that a Polarizer, Analyzer and/or Compensator(s) can be rotated during data acquisition, and are describe variously as Rotating Polarizer (RPE), Rotating Analyzer (RAE) and Rotating Compensator (RCE) Ellipsometer Systems.
Where an ellipsometer system is applied to investigate a small region of a material system present, it must be appreciated that the beam of electromagnetic radiation can be convergently entered thereto through an input lens, and, optionally, exit via a re-collimating output lens. In effect this adds said input, go (and output), lenses as elements in the ellipsometer system as xe2x80x9cadditional elementsxe2x80x9d, (eg. identified in d. and f. above), which additional elements must be accounted for in the mathematical model. If this is not done, material system representing parameters determined by application of the ellipsometer system and mathematical regression, will have the effects of said input, (and output), lenses at least partially correlated thereinto, much as if the input and, (output lenses), were integrally a part of the material system.
It is emphasized that where two sequentially adjacent elements in an ellipsometer system are held in a static positon with respect to one another while experimental ellipsometric data is acquired, said two sequentially adjacent elements generally appear to be a single element. Hence, a beam directing element adjacent to a lens can appear indistinguishable from said lens as regards the overall effect of said combination of elements. In that light it is to be understood that present input and output lenses are normally structurally fixedly positioned and are not rotatable with respect to a material system present in use, thus preventing breaking correlation between parameters in equations for sequentially adjacent input and output lenses and an investigated material system by an element rotation technique. While correlation of parameters in mathematical equations which describe the effects of groupings of elements, (such as a compensator and an optional element(s)), can be tolerable, correlation between parameters in the mathematical model of an investigated material system and other elements in the ellipsometer system must be broken to allow obtaining accurate material system representing PSI and DELTA values, emphasis added. That is to say that correlation between parameters in equations in a mathematical model which describe the effects of a stationary compensator and a sequentially next located lens element, (eg. correllation between effects of elements c. and d. or between f. and g. identified above), in a beam of electromagnetic radiation might be tolerated to the extent that said correlation does not influence determination of material system describing PSI and DELTA values, but the correlation between parameters in equations which describe the effects of ellipsometer system components (eg. a., b., c., d., f., g., h. and i.), and equations which describe the effects of a present material system (eq. element e. above), absolutely must be broken to allow the ellipsometer system to provide accurate PSI and DELTA values for said material system. Application of ellipsometry to investigation of a material system present can then present a challenge to users of ellipsometer systems in the form of providing a mathematical model for each of an input and output lens, and providing a method by which the effects of said input and output lenses can be separated from the effects of an investigated material system.
Thus is identified an example of a specific problem, solution of which is the topic of the present invention.
One typical approach to overcoming the identified problem, where space considerations are not critical, and where ellipsometer system configuration can be easily modified, is to obtain multiple data sets with an ellipsometer system configured differently during at least two different data set acquisitions. For instance, a data set can be obtained with a material system present and in which a beam of electromagnetic radiation is caused to interact with said material system, and another data set can be obtained with the ellipsometer system configured in a straight-through configuration, where a beam of electromagnetic radiation is caused to pass straight through an ellipsometer system without interacting with a material system. Simultaneous mathematical regression utilizing multiple data sets can allow evaluation of material system characterizing PSI and DELTA values over a range of wavelengths, uncorrelated with present birefringent retardation effects of present input and output lenses. The problem with this approach is that where ellipsometer systems are fit to vacuum chambers for instance, ellipsometer reconfiguration so as to allow acquisition of such multiple data sets can be extremely difficult, if not impossible to carry out.
Another rather obvious solution to the identified problem is to provide input, and output, lenses which are absolutely birefringence-free, and transparent at all electromagnetic beam wavelengths utilized. That is, provide input, and output, lenses which do not attenuate the magnitude of rp or rs orthogonal components, (or at least do not change their ratio, rp/rs), and which also do not enter phase shift between rp or rs orthogonal components when said beam of electromagnetic radiation is caused to pass therethrough. While control of the the effect of a lens on a ratio, (rp/rs), of electromagnetic beam orthogonal components can often rather successfully be accomplished by causing a beam of electromagnetic radiation to approach a surface of a lens along essential a normal to a surface thereof, this is not the case regarding phase shift entered between rp and rs orthogonal components of a said beam of electromagnetic radiation caused to pass therethrough. That is, input, and output, lenses can demonstrate xe2x80x9cbirefringencexe2x80x9d, in that the rp orthogonal component is xe2x80x9cretardedxe2x80x9d by a different amount than is the rs orthogonal component when said beam of electromagnetic radiation is caused to pass therethrough. To complicate matters, this xe2x80x9cbirefringentxe2x80x9d effect also varies with wavelength and with stresses which can develop in a lens during use because of temperature and physical changes etc.
As described in Parent application Ser. No. 09/162,217, (which is incorporated herein by reference), controlling stress related change is presently achieved with varying degrees of success, where for instance, windows in a vacuum chamber are subject. Windows provided by BOMCO Inc. are produced with the goal of eliminating birefringence, and are mounted in vacuum chambers using copper gasket seals which help to minimize uneven application of stresses and developed strains thereacross. While some success is achieved via this approach, the BOMCO windows are not xe2x80x9cperfectxe2x80x9d and do demonstrate some remaining birefringence properties, which can vary in unpredictable ways over a period of usage. In addition, BOMCO windows are expensive,(costing on the order of $1000.00 each), and are large in size thereby making adaptation thereof to use in a vacuum chamber difficult at times, particularly in retro-fit scenarios. And, there have been cases where BOMCO windows have broken in use. This is highly undesirable as vacuum chambers are often times caused to contain highly toxic and hazardous materials during, for instance, etching and/or deposition steps required in the fabrication of semiconductor devices. Where vacuum chamber windows are the subject, an alternative to use of the BOMCO windows is to simply use standard vacuum chamber windows, which, while significantly less expensive, demonstrate order of magnitude larger birefringence effects. (Note, BOMCO windows provide birefringent effects on the order of approximately six-tenths (0.6) to two-tenths (0.2) degrees over a range of wavelengths of from four-hundred (400) to seven-hundred-fifty (750) nanometers, whereas standard vacuum windows demonstrate birefringent effects on the order of six (6.0) to three (3.0) degrees over the same range of wavelengths). (Note, birefringent retardation typically follows an approximate inverse wavelength, (eg. 1/wavelength), relationship). However, where standard vacuum chamber windows are utilized, compensation of their effects is required. Similar concerns apply where input and output lenses, and associated ellipsometrically indistinguishable ellipsometer system components are concerned.
A need is thus identified for a method of practicing ellipsometry which enables the breaking of correlation between parameters in equations which describe retardance entered to orthogonal components of a beam of electromagnetic radiation caused to interact with a material system, and parameters in equations which describe birefringent effects on said orthogonal components in said beam of electromagnetic radiation caused by input and output windows of a vacuum chamber, and/or by input and output lenses and/or by electromagnetic beam directing means etc.
Various researchers have previously noted the identified problem, where vacuum chamber windows are the topic, and proposed various first order mathematical model equation correction techniques as solution, which approaches have met with various degrees of success where vacuum chamber input and output windows demonstrate on the order of a maximum of two (2) degrees of birefringence. This, however, leaves the problem unsolved where birefringence approaches six (6.0) degrees, as commonly occures in standard vacuum chamber windows, and can also occur in lens systems, particlarly at wavelengths of four-hundred (400) nanometers and below. Thus is identified a problem to which the present invention calibration methodology applies.
Patents of which the Inventor is aware include U.S. Pat. No. 5,757,494 to Green et al., in which is taught a method for extending the range of Rotating Analyzer/Polarizer ellipsometer systems to allow measurement of DELTAS near zero (0.0) and one-hundred-eighty (180) degrees. Said Patent describes the presence of a window-like variable birefringent components which is added to a Rotating Analyzer/Polarizer ellipsometer system, and the application thereof during data acquisition, to enable the identified capability.
A Patent to Thompson et al. U.S. Pat. No. 5,706,212 teaches a mathematical regression based double fourier series ellipsometer calibration procedure for application, primarily, in calibrating ellipsometers system utilized in infrared wavelength range. Birefringent window-like compensators are described as present in the system thereof, and discussion of correlation of retardations entered by sequentially adjacent elements which do not rotate with respect to one another during data acquisition is described therein.
A Patent to Woollam et al, U.S. Pat. No. 5,582,646 is disclosed as it describes obtaining ellipsometic data through windows in a vacuum chamber, utilizing other than a Brewster Angle of Incidence.
Patent to Woollam et al, U.S. Pat. No. 5,373,359, Patent to Johs et al. U.S. Pat. No. 5,666,201 and Patent to Green et al., U.S. Pat. No. 5,521,706, and Patent to Johs et al., U.S. Pat. No. 5,504,582 are disclosed for general information as they pertian to Rotating Analyzer ellipsometer systems.
Patents identified in a Search specifically focused on the use of lenses, preferrably achromatic, in ellipsometry and related systems are:
U.S. Pat. Nos. 5,877,859 and 5,798,837 to Aspnes et al.;
U.S. Pat. No. 5,333,052 to Finarov;
U.S. Pat. No. 5,608,526 to Piwonka-Corle et al.;
U.S. Pat. No. 5,793,480 to Lacy et al.;
U.S. Pat. Nos. 4,636,075 and 4,893,932 to Knollenberg; and
U.S. Pat. No. 4,668,860 to Anthon.
The most relevant Patent found is U.S. Pat. No. 5,917,594 to Norton. However, the system disclosed therein utilizes a spherical mirror to focus an electromagentic beam onto the surface of a sample in the form of a small spot. Said system further develops both reflection and transmission signals via application of reflective means and of reflection and transmission detectors. The somewhat relevant aspect of the 594 Patent system is that a positive lens and a negative meniscus lens are combined and placed into the pathway of the electromagnetic beam prior to its reflection from a focusing spherical mirror. The purpose of doing so is to make the optical system, as a whole, essentially achromatic in the visible wavelength range, and even into the ultraviolet wavelength range. It is further stated that the power of the combined positive lens and negative meniscus lens is preferrably zero. It is noted that, as described elsewhere in this Specification, said 594 Patent lens structure, positioning in the 594 Patent system, and purpose thereof are quite distinct from the present invention lens structure and application to focus a beam of electromagnetic radiation. In particular, note that the 594 Patent lens is not applied to directly focus and/or recollimate a beam of electromagnetic radiation onto a sample system, as do the lenses in the present invention. And, while the present invention could utilize a meniscus lens in an embodiment thereof, the 594 Patent specifically requires and employs a negative meniscus lens to correct for spherical aberabtions caused by off-axis reflection from a spherical mirror, in combination with a positive lens to correct for achromatic aberation introduced by said negative meniscus lens. Further, the present invention system does not require reflection means be present in the path of an electromagnetic beam after its passage through the focusing lens thereof and prior to interacting with a sample system, as does the system in the 594 Patent wherein a focusing spherical mirror is functionally required.
Various papers were also identified as possibly pertinant, and are:
A paper by Johs, titled xe2x80x9cRegression Calibration Method for Rotating Element Ellipsometersxe2x80x9d, Thin Solid Films, 234 (1993) is also disclosed as it describes a mathematical regression based approach to calibrating ellipsometer systems.
A paper by Nijs and Silfhout, titled xe2x80x9cSystematic and Ramdom Errors in Rotating-Analyzer Ellipsometryxe2x80x9d, J. Opt. Soc. Am. A., Vol. 5, No. 6, (June 1988), describes a first order mathematical correction factor approach to accounting for window effects in Rotating Analyzer ellipsometers.
A paper by Kleim et al, titled xe2x80x9cSystematic Errors in Rotating-Compensator ellipsometryxe2x80x9d, J. Opt. Soc. Am., Vol 11, No. 9, (setp. 1994) describes first order corrections for imperfections in windows and compensators in Rotating Compensator ellipsometers.
Other papers of interest in the area by Azzam and Bashara include one titled xe2x80x9cUnified Analysis of Ellipsometry Erors Due to Imperfect Components Cell-Window Birifringence, and Incorrect Azimuth Anglesxe2x80x9d, J. of the Opt. Soc. Am., Vol 61, No. 5, (May 1971) and one titled xe2x80x9cAnalysis of Systematic Errors in Rotating-Analyzer Ellipsometersxe2x80x9d, J. of the Opt. Soc. Am., Vol. 64, No. 11, (Nov. 1974).
Another paper by Straaher et al, titled xe2x80x9cThe Influence of Cell Window Imperfections on the Calibration and Measured Data of Two Types of Rotating Analyzer Ellipsometersxe2x80x9d, Surface Sci., North Holland, 96, (1980), describes a graphical method for determining a plane of incidence in the presence of windows with small retardation.
A paper by Jones titled xe2x80x9cA New Calculus For The Treatment of Optical Systemsxe2x80x9d, J.O.S.A., Voil. 31, (July 1941), is also identified as it describes the characterizing of multiple lens elements which separately demonstrate birefringence, as a single lens, (which can demonstrate reduced birefringence).
Finally, a paper which is co-authored by inventors herein is titled xe2x80x9cIn Situ Multi-Wavelength Ellipsometric Control of Thickness and Composition of Bragg Reflector Structuresxe2x80x9d, by Herzinger, Johs, Reich, Carpenter and Van Hove, Mat. Res. Soc. Symp. Proc., Vol. 406, (1996) is also disclosed.
Even in view of relevant prior art, there remains need for ellipsometer systems which comprise input, and optionally output, lenses that allow focusing spectroscopic electromagnetic beams as small spots on material substrates. Further, in view of the inability of first order corrections to break birefringence based correlation between input and/or output lenses and a material system, there remains need for a second order mathematical model equation correction technique which enables breaking correlation between a material system characterizing DELTA and in-plane retardance entered to a beam of electromagnetic radiation by input and output lenses through which said beam of electromagnetic radiation is caused to pass. This is particularly true where lens birefringent retardance exceeds a few degrees. The present invention responds to said identified needs.
The present invention system basically comprises a lens system, primarily as applied in ellipsometer and polarimeter systems wherein birefringence, and spectroscopic electromagnetic beam spot size chromatic dispersion reduction and focal length chromatic dispersion reduction is desired, but wherein spherical, coma distortion, third order aberations, astigmatism and image reproduction are substantially unimportant considerations. A single stage present invention lens system has a focal length of one-hundred millimeters or less, (nominally about eighty millimeters), and said lens system comprises two sequentially oriented elements, one of said two sequentially oriented elements being of a shape and orientation which individually converges a beam of electromagnetic radiation caused to pass therethrough, and the other being of a shape and orientation which individually diverges, (to a lesser degree than said convergence), a beam of electromagnetic radiation caused to pass therethrough, there being a region between said first and second elements. A present invention dual stage lens system provides a less than fifty millimeter, (nominal about forty millimeter), focal length and is comprised of four sequentially oriented lens elements which are grouped into two groups of two elements each, two of which four elements are converging and two of which are diverging of electromagenic radiation caused to pass therethrough.
It is to be understood that, in use, a beam of electromagnetic radiation sequentially passes through one of said first and second elements in a single present invention lens system, then said region therebetween, and then through said second of said first and second elements before emerging as a focused beam of electromagnetic radiation, said region between said first and second elements have essentially the optical properties of a void region, or functional equivalent. In a dual stage present invention lens system a second stage of first and second elements is present in the electromagnetic beam pathway.
Further, present invention lens systems are characterized as quasi-achromatic as a result of multi-element construction, wherein, for each said two element lens systems present, the two elements thereof are made from different materials, (eg. one from what is commonly termed Crown-glass and one from Flint-glass in the literature). Again, as a result of present invention lens construction, very small electromagnetic beam spot focusing on an investigated material system is possible over a large range of wavelengths, (including transmitting properties into the deep UV), because of reduced chromatic focal length and spot size dispersion. It is noted that said present invention multi-element ellipsometer system input (and output) lenses can both (when present) demonstrate birefringence; neither demonstrate birefringence or one can demonstrate birefringence and the other not demonstrate birefringence. In fact, one non-birefringent input or output lens can be absent but for a consideration of its presence as essentially surrounding atmospheric ambient, or equivalent thereto.
A present invention lens system, which is particulary well suited for application in ellipsometer systems, provides for spectroscopic electromagnetic beam spot size and focal length chromatic dispersion reduction by configuring at least two sequentially oriented elements, one of said at least two sequentially oriented elements being of a shape and orientation which individually converges a beam of electromagnetic radiation caused to pass therethrough, and the other being of a shape and orientation which individually diverges a beam of electromagnetic radiation caused to pass therethrough, there being a region between said first and second elements such that, in use, a beam of electromagnetic radiation sequentially passes through said first element, then said region therebetween, and then said second element before emerging as a focused beam of electromagnetic radiation. Such a lens system with application in ellipsometer systems is characterized by a converging element which presents as a selection from the group consisting of:
a bi-convex;
a plano-convex with an essentially flat side;
and said diverging element is characterized as a selection from the group consisting of:
a bi-concave lens element;
a plano-concave with an essentially flat side.
Further, as shown in FIGS. 1a7-1a24, said present invention lens systems can comprise a selection from the group consisting of:
a) a sequential combination of a bi-convex element and a bi-concave element;
b) a sequential combination of a bi-concave element and a bi-convex element;
c) a sequential combination of a bi-convex element and a plano-concave element with said concave side of said plano-concave element adjacent to said bi-convex element;
d) a sequential combination of a bi-convex element and a plano-concave element with said essentially flat side of said plano-concave element being adjacent to said bi-convex element;
e) a sequential combination of a plano-concave element and a bi-convex element with said essentially flat side of said plano-concave element adjacent to said bi-concave element;
f) a sequential combination of a plano-concave element and bi-convex element with said concave side of said plano-concave element adjacent to said bi-convex element;
g) a sequential combination of a plano-convex element and a bi-concave element with said essentially flat side of said plano-convex element adjacent to said bi-concave element;
h) a sequential combination of a bi-concave element with a plano-convex element with said convex side of said plano-convex element adjacent to said bi-concave element;
i) a sequential combination of a piano-concave element and a plano-convex element with the essentially flat side of said plano-concave element being adjacent to the convex side of the plano-convex element;
j) a sequential combination of a plano-concve element and a plano-convex element with the essentially flat side of said plano-concave element being adjacent to the convex side of said plano-convex element;
k) a sequential combination of a plano-convex element and a plano-concave element with the essentially flat side of said plano-covex element and the essentially flat side of said plano-concave element being adjacent to one another;
l) a sequential combination of a plano-concave element and a plano-convex element with the concave side of said plano-concave element being adjacent to the convex side of the plano-convex element;
m) a sequential combination of a plano-convex element and a bi-concave element with said convex side of said plano-convex element adjacent to said bi-concave element;
n) a sequential combination of a bi-concave element and a plano-convex element with said essentially flat side of said plano-convex element adjacent to said bi-concave element;
o) a sequential combination of a plano-convex element and a plano-concave element with said convex side of said plano-convex element adjacent to the concave side of the plano-concave element;
p) a sequential combination of a plano-concave element and a plano-convex element with said essentially flat side of said plano-convex element being adjacent to the essentially flat side of the plano-concave element;
q) a sequential combination of a plano-convex element and a plano-concave element with said convex side of said plano-convex element being adjacent to the essentially flat side of the plano-concave element; and
r) a sequential combination of a plano-concave element with a plano-convex element with the essentially flat side of said plano-convex element being adjacent to the concave side of said plano-concave element;
and wherein said region between said first and second elements having essentially the optical properties of a selection from the group consisting of:
a void region; and
a functional equivalent to a void region.
A present invention lens system with application in ellipsometer systems can be further characterized in that the converging element of said first and second elements is typically made of a material independently selected from the group consisting of:
CaF2;
BaF2;
LiF; and
MgF2;
and the diverging element of said first and second elements is selected to be made of fused silica, although it is within the scope of the present invention to make the converging element of fused silica and the diverging element of a selection from the group consisting of CaF2; BaF2; LiF; and MgF2. It is noted that lens elements made of MgF2 are typically bi-refringent whereas lens elements made of CaF2; BaF2 and LiF typically demonstrate far less bi-refringence, unless subjected to stress.
A present invention lens system with a focal lenght of fifty millimeters or less, with application in ellipsometer systems, can be described as being comprised of lens system comprising two sequentially oriented lenses, each of said sequentially oriented lenses being comprised of:
at least two sequentially oriented elements, one of said at least two sequentially oriented elements being of a shape and orientation which individually converges a beam of electromagnetic radiation caused to pass therethrough, and the other being of a shape and orientation which individually diverges a beam of electromagnetic radiation caused to pass therethrough, there being a region between said first and second elements such that, in use, a beam of electromagnetic radiation sequentially passes through said first element, then said region therebetween, and then said second element before emerging as a focused beam of electromagnetic radiation; said lens system being described by a selection, as shown in FIGS. 1a25-1a28, from the group consisting of:
1. a sequential combination of a converging element (C), a diverging element (D), a converging element (C) and a diverging element (D);
2. a sequential combination of a converging element (C), a diverging (D) element, a diverging (D), element and a converging (C) element;
3. a sequential combination of a diverging element (D), a converging element (C), a diverging (D) element and a converging (C) element;
4. a sequential combination of a diverging element (D), a converging element (C), a converging element (C) and a diverging (D) element.
And, of course, other sequential lens element configurations within the scope of the present invention include:
(Converging(C))(Converging(C)(Diverging();
(Diverging(D))(Diverging(D))(Converging(C);
(Converging(C))(Diverging(D))(Diverging(D));
(Diverging(D))(Converging(C))(Diverging(DD));
(Converging(C))(Converging(C)(Diverging(D))(Diverging(D)); and
(Diverging(D)(Diverging(D))(Converging(C))(Converging(C)).
One embodiment of a present invention lens system is further characterized by at least one selection from the group consisting of:
a. the focal length of the lens system is between forty (40) and forty-one (41) millimeters over a range of wavelengths of at least two-hundred (200) to seven-hundred (700) nanometers; and
b. the focal length of the dual stage lens system varies by less than five (5%) percent over a range of wavelengths of between two-hundred and five-hundred nanometers; and
c. the spot diameter at the focal length of the lens system is less than seventy-five (75) microns over a range of wavelengths of at least two-hundred (200) to seven-hundred (700) nanometers.
(It is noted that the listing of single two element lens constructions (a) through (r) above provides insight to applicable converging and diverging lens element combinations in dual stage lens systems).
It is specifically noted that the present invention includes the case of an ellipsometer system in which only one of said multi-element input or output lenses is present, (typically only the input lens), and the case wherein both input and output lenses are present, but only one is of multiple element construction, and/or demonstrates bi-refringence.
A prefered present invention single two element lens system is constructed from a Bi-convex lens element made of CaF2, (eg. JANOS Technology Inc. Part No. A1407-003), functionally combined with a Fused Silica Plano-Concave lens element, (eg. OptoSigma Inc. Part No. 012-0080), in a manner generally indicated by FIG. 1a3.
Continuing, it is further noted that various beam directing means, such as mirror systems, enable providing small, spectroscopically essentially undispersed, electromagnetic beam spot size at a material system, but that most such mirror systems are birefringent, in that they retard orthogonal components of a polarized electromagnetic beam reflecting therefrom, by different amounts.
Further, while present invention multi-element lenses in ellipsometric settings are typically relatively less birefringent and chromatically dispersive than are, for instance, electromagnetic beam directing mirror systems, in the case where a present invention multi-element input and/or output optical element(s) demonstrates birefringence, the present invention is further a method of accurately evaluating parameters in parameterized equations in a mathematical model of a system of spatially separated input and output elements, (herein beneficially, demonstratively, identified as lenses), as applied in an ellipsometry or polarimetry setting. Said parameterized equations enable, when parameters therein are properly evaluated, independent calculation of retardation entered by each of said multi-element input lens and said multi-element output lens to, or between, orthogonal components of a beam of electromagnetic radiation caused to pass through said input and output lenses. This provides utility in the form of enabling the breaking of correlation between retardation entered between orthogonal components in a spectroscopic electromagetic beam by input and output lenses and by a material system under investigation. (It is to be understood that at least one of said multi-element input and output lenses in a present invention ellipsometer is often at least somewhat birefringent even though it is quasi-achromatic regarding focal length over a relativley wide wavelength range).
In a basic sense, the present invention method of breaking correlation between retardation effects caused by present invention multi-element input and/or output lenses in an ellipsometer system, and retardation effects caused by an adjacent, otherwise ellipsometrically undistinguishable material system being investigated comprises, in any functional order, the steps of:
a. providing spatially separated input and output optical element (eg. lenses), at least one of said input output lenses demonstrating birefringence when a beam of electromagnetic radiation is caused to pass therethrough, there being a means for supporting a material system positioned between said input and output lenses;
b. positioning an ellipsometer system source of electromagnetic radiation and an ellipsometer system detector system such that in use a beam of electromagnetic radiation provided by said source of electromagnetic radiation is caused to pass through said input lens, interact with said material system in a plane of incidence thereto, and exit through said output lens and enter said detector system;
c. providing a material system to said means for supporting a material system, the composition of said material system being sufficiently well known so that retardance entered thereby to a polarized beam of electromagnetic radiation of a given wavelength, which is caused to interact with said material system in a plane of incidence thereto, can be accurately modeled mathematically by a parameterized equation which, when parameters therein are properly evaluated, allows calculation of retardance entered thereby between orthogonal components of a beam of electromagnetic radiation caused to interact therewith in a plane of incidence thereto, given wavelength;
d. providing a mathematical model for said ellipsometer system and said input and output lenses and said material system, comprising separate parameterized equations for independently calculating retardance entered between orthogonal components of a beam of electromagnetic radiation caused to pass through each of said input and output lenses and interact with said material system in a plane of incidence thereto; such that where parameters in said mathematical model are properly evaluated, retardance entered between orthogonal components of a beam of electromagnetic radiation which passes through each of said input and output lenses and interacts with said material system in a plane of incidence thereto can be independently calculated from said parameterized equations, given wavelength;
e. obtaining a spectroscopic set of ellipsometric data with said parameterizable material system present on the means for supporting a material system, utilizing a beam of electromagnetic radiation provided by said source of electromagnetic radiation, said beam of electromagnetic radiation being caused to pass through said input lens, interact with said parameterizable material system in a plane of incidence thereto, and exit through said output lens and enter said detector system;
f. by utilizing said mathematical model provided in step d. and said spectroscopic set of ellipsometric data obtained in step e., simultaneously evaluating parameters in said mathematical model parameterized equations for independently calculating retardance entered between orthogonal components in a beam of electromagnetic radiation caused to pass through said input lens, interact with said material system in a plane of incidence thereto, and exit through said output lens.
The end result of practice of said method is that application of said parameterized equations for each of said input lens, output lens and material system for which values of parameters therein have been determined in step f., enables independent calculation of retardance entered between orthogonal components of a beam of electromagnetic radiation by each of said input and output lenses, and said material system, at given wavelengths in said spectroscopic set of ellipsometric data. And, it is emphasized that said calculated retardance values for each of said input lens, output lens and material system are essentially uncorrelated.
It is further to be appreciated that one of said input or output lenses can be physically absent entirely, which is the equivalent to considering it to be simply surrounding ambient atmosphere with associated non-birefringent properties. The language xe2x80x9cproviding spatially separated input and output lenses, at least one of said input and output lenses demonstrating birefringence when a beam of electromagnetic radiation is caused to pass therethroughxe2x80x9d, is to be interpreted to include such a situation wherein a non-birefringent lens is simply atmospheric ambient or an optical equivalent. Additionally, it is to be understood that input optical elements can comprise beam directing means and window(s), (as in a vacuum chamber), in addition to input lens(es); and that optput optical elements can comprise selection beam directing means and window(s), (as in a vacuum chamber), as well as output lens(es).
As further discussed later herein, a modification to the just recited method can be to, (in the step d. provision of a mathematical model for said ellipsometer system and said input and output lenses and said parameterizable material system for each of said input and output lenses), provide separate parameterized mathematical model parameterized equations for retardance entered to each of said two orthogonal components of a beam of electromagnetic radiation caused to pass through said input and output lenses. When this is done, at least one of said orthogonal components for each of said input and output lenses is directed out of the plane of incidence of said electromagnetic beam onto said parameterizable material system. And, typically, though not necessarily, one orthogonal component will be aligned with the plane of incidence of said electromagnetic beam onto said parameterizable material system. When this is done, calculation of retardation entered between orthogonal components of said beam of electromagnetic radiation, given wavelength, by said input lens is provided by comparison of retardance entered to each of said orthogonal components for said input lens, and such that calculation of retardation entered between orthogonal components of said beam of electromagnetic radiation, given wavelength, by said output lens is provided by comparison of retardance entered to each of said orthogonal components for said output lens.
It is pointed out that the step f. simultaneous evaluation of parameters in said mathematical model parameterized equations for said parameterizable material system, and for said input and output lenses, is typically, though not necessarily, achieved by a square error reducing mathematical curve fitting procedure.
It is important to understand that in the method recited earlier, the step b. positioning of an ellipsometer system source of electromagnetic radiation and an ellipsometer system detector system includes positioning a polarizer between said source of electromagnetic radiation and said input lens, and the positioning of an analyzer between said output lens and said detector system, and in which the step e. obtaining of a spectroscopic set of ellipsometric data typically involves obtaining data at a plurality of settings of at least one component selected from the group consisting of: (said analyzer and said polarizer). As well, it is to be understood that additional elements can also be placed between said source of electromagnetic radiation and said input lens, and/or between said output lens and said detector system, and that the step e. obtaining of a spectroscopic set of ellipsometric data can involve, alternatively or in addition to the recited procedure, obtaining data at a plurality of settings of at least one of said additional components.
It is also to be understood that the step of providing separate parameterized mathematical model parameterized equations for enabling independent calculation of retardance entered by said input said output lenses between orthogonal components of a beam of electromagnetic radiation caused to pass through said input and output lenses preferably involves parameterized equations having a form selected from the group consisting of:             ret      ⁡              (        λ        )              =          (              K1        /        λ            )                  ret      ⁡              (        λ        )              =                  (                  K1          /          λ                )            *              (                  1          +                      (                          K2              /                              λ                2                                      )                          )                        ret      ⁡              (        λ        )              =                  (                  K1          /          λ                )            *              (                  1          +                      (                          K2              /                              λ                2                                      )                    +                      (                          K3              /                              λ                4                                      )                          )            
A modified method of accurately evaluating parameters in parameterized equations in a mathematical model of a system of spatially separated input and output lenses, said parameterized equations enabling, when parameters therein are properly evaluated, independent calculation of retardation entered by each of said input lens and said output lens to at least one orthogonal component(s) of a beam of electromagnetic radiation caused to pass through said input and output lenses, at least one of said input and output lenses being birefringent, said method comprising, in a functional order, the steps of:
a. providing spatially separated input and output lenses, at least one of said input and output lenses demonstrating birefringence when a beam of electromagnetic radiation is caused to pass therethrough, there being a means for supporting a material system positioned between said input and output lenses;
b. positioning an ellipsometer system source of electromagnetic radiation and an ellipsometer system detector system such that in use a beam of electromagnetic radiation provided by said source of electromagnetic radiation is caused to pass through said input lens, interact with said material system in a plane of incidence thereto, and exit through said output lens and enter said detector system;
c. providing a material system to said means for supporting a material system;
d. providing a mathematical model for said ellipsometer system and said input and output lenses and said material system, comprising, for each of said input lens and said output lens, separate parameterized equations for retardance for at least one orthogonal component in a beam of electromagnetic radiation provided by said source of electromagnetic radiation, which orthogonal component is directed out of a plane of incidence which said electromagnetic beam makes with said material system in use, and optionally providing separate parameterized equations for retardance for an in-plane orthogonal component of said beam of electromagnetic radiation, such that retardation entered to said out-of-plane orthogonal component, and optionally to said in-plane orthogonal component, of said beam of electromagnetic radiation by each of said input and output lenses, can, for each of said input and output lenses, be separately calculated by said parameterized equations, given wavelength, where parameters in said parameterized equations are properly evaluated;
e. obtaining a spectroscopic set of ellipsometric data with said material system present on the means for supporting a material system, utilizing a beam of electromagnetic radiation provided by said source of electromagnetic radiation, said beam of electromagnetic radiation being caused to pass through said input lens, interact with said material system in a plane of incidence thereto, and exit through said output lens and enter said detector system;
f. by utilizing said mathematical model provided in step d. and said spectroscopic set of ellipsometric data obtained in step e., simultaneously evaluating material system DELTA""S in correlation with in-plane orthogonal component retardation entered to said beam of electromagnetic radiation by each of said input and output lenses, and parameters in said mathematical model parameterized equations for out-of-plane retardance entered by said input lens and said output lens to a beam of electromagnetic radiation caused to pass through said input lens, interact with said material system in said plane of incidence thereto, and exit through said output lens.
Again, application of said parameterized equations for out-of-plane retardance entered by said input lens and said output lens to a beam of electromagnetic radiation caused to pass through said input lens, interact with said material system in said plane of incidence thereto, and exit through said output lens, for which values of parameters therein are determined in step f., enables independent calculation of retardance entered to said out-of-plane orthogonal component of a beam of electromagnetic radiation by each of said input and output lenses, given wavelength.
Also, again the step f. simultaneous evaluation of parameters in said mathematical model parameterized equations for calculation of retardance entered to said out-of-plane orthogonal component of a beam of electromagnetic radiation by each of said input and output lenses, given wavelength, and said correlated material system DELTA""S and retardance entered to said in-plane orthogonal component of a beam of electromagnetic radiation by each of said input and output lenses, is typically achieved by a square error reducing mathematical curve fitting procedure.
It remains, in the presently disclosed method, to provide values for parameters in the in-plane parameterized equations for retardation, in said mathematical model of a system of spatially separated input and output lenses. The presently disclosed method therefore further comprises the steps of:
g. providing a parameterized equation for retardation entered by said material system to the in-plane orthogonal component of a beam of electromagnetic radiation, and as necessary similar parameterized equations for retardation entered by each of said input and output lenses to the in-plane orthogonal component of a beam of electromagnetic radiation; and
h. by utilizing said parameterized mathematical model provided in step d. and said spectroscopic set of ellipsometric data obtained in step e., simultaneously evaluating parameters in said mathematical model parameterized equations for independent calculation of retardance entered in-plane by said material system and by said input lens and said output lens such that the correlation between material system DELTA""S and the retardance entered by said in-plane orthogonal component of a beam of electromagnetic radiation by each of said input and output lenses, at given wavelengths in said spectroscopic set of ellipsometric data, is broken.
The end result of practice of the immediately foregoing steps a.-h. is that application of said parameterized equations for each of said input lens, output lens and material system for which values of parameters therein have been determined in step h., enables independent calculation of retardance entered to both said out-of-plane and said in-plane orthogonal components of a beam of electromagnetic radiation by each of said input and output lenses, and retardance entered by said material system to said in-plane orthogonal component of said beam of electromagnetic radiation, at given wavelengths in said spectroscopic set of ellipsometric data.
As before for other parameter evaluation steps, the step h. simultaneous evaluation of parameters in said mathematical model parameterized equations for said in-plane retardation entered by said parameterized material system, and said input and output lenses, is typically achieved by a square error reducing mathematical curve fitting procedure.
If the material system present can not be easily parameterized, the presently disclosed method of accurately evaluating parameters in parameterized equations in a mathematical model of a system of spatially separated input and output lenses, provides that the following steps, g.-j. be practiced:
g. removing the material system from said means for supporting a material system positioned between said input and output lenses, and positioning in its place an alternative material system for which a parameterized equation for calculating in-plane retardance entered to a beam of electromagnetic radiation, given wavelength, can be provided;
h. providing a parameterized equation for retardation entered in-plane to an orthogonal component of a beam of electromagnetic radiation by said alternative material system which is then positioned on said means for supporting a material system positioned between said input and output lenses, and as necessary similar parameterized equations for retardation entered by each of said input and output lenses to the in-plane orthogonal component of a beam of electromagnetic radiation;
i. obtaining a spectroscopic set of ellipsometric data with said alternative material system present on the means for supporting a material system, utilizing a beam of electromagnetic radiation provided by said source of electromagnetic radiation, said beam of electromagnetic radiation being caused to pass through said input lens, interact with said alternative material system in a plane of incidence thereto, and exit through said output lens and enter said detector system;
j. by utilizing said parameterized mathematical model for said input lens and said output lens provided in step d. and said parameterized equation for retardation entered by said alternative material system provided in step h., and said spectroscopic set of ellipsometric data obtained in step i., simultaneously evaluating parameters in said mathematical model parameterized equations for independent calculation of retardance entered to an in-plane orthogonal component of said beam of electromagnetic radiation by said alternative material system and by said input lens and said output lens, such that correlation between DELTA""S entered by said alternative material system and retardance entered by said in-plane orthogonal component of said beam of electromagnetic radiation, by each of said input and output lenses, at given wavelengths in said spectroscopic set of ellipsometric data, is broken, said simultaneous evaluation optionally providing new values for parameters in parameterized equations for calculation of retardance entered in said out-of-plane components of said beam of electromagnetic radiation by each of said input lens and said output lens;
The end result being that application of said parameterized equations for each of said input lens and output lens and alternative material system, for each of which values of parameters therein have been determined in step j., enables independent calculation of retardance entered to both said out-of-plane and said in-plane orthogonal components of a beam of electromagnetic radiation by each of said input lens and said output lens, and retardance entered by said alternative material system to said in-plane orthogonal component of a beam of electromagnetic radiation, at given wavelengths in said spectroscopic set of ellipsometric data.
As before, said presently disclosed method of accurately evaluating parameters in parameterized equations in a mathematical model of a system of spatially separated input and output lenses provides that in the step j. simultaneous evaluation of parameters in said mathematical model parameterized equations for said in-plane retardation entered by said parameterized material system, and at least said in-plane input lens and output lens, is typically achieved by a square error reducing mathematical curve fitting procedure.
As mentioned with respect to the first method of the present invention disclosed herein, the presently disclosed method of accurately evaluating parameters in parameterized equations in a mathematical model of a system of spatially separated input and output lenses provides that the step b. positioning of an ellipsometer system source of electromagnetic radiation and an ellipsometer system detector system includes positioning a polarizer between said source of electromagnetic radiation and said input lens, and the positioning of an analyzer between said output lens and said detector system, and in which the step e. obtaining of a spectroscopic set of ellipsometric data involves obtaining data at a plurality of settings of at least one component selected from the group consisting of: (said analyzer and said polarizer). As well, it is again to be understood that additional elements can also be placed between said source of electromagnetic radiation and said input lens, and/or between said output lens and said detector system, and that the step e. obtaining of a spectroscopic set of ellipsometric data can involve, alternatively or in addition to the recited procedure, obtaining data at a plurality of settings of at least one of said additional components.
Said presently disclosed method of accurately evaluating parameters in parameterized equations in a mathematical model of a system of spatially separated input and output lenses also provides that the step of providing separate parameterized mathematical model parameterized equations for enabling independent calculation of out-of-plane and in-plane retardance entered by said input said output lenses to said beam of electromagnetic radiation caused to pass through said input and output lenses involve parameterized equations having a form selected from the group consisting of:             ret      ⁡              (        λ        )              =          (              K1        /        λ            )                  ret      ⁡              (        λ        )              =                  (                  K1          /          λ                )            *              (                  1          +                      (                          K2              /                              λ                2                                      )                          )                        ret      ⁡              (        λ        )              =                  (                  K1          /          λ                )            *              (                  1          +                      (                          K2              /                              λ                2                                      )                    +                      (                          K3              /                              λ                4                                      )                          )            
It is again noted that while the present invention can be practiced with any type xe2x80x9clensesxe2x80x9d, be there one or two of them, (ie. one, or both, of the input or output lenses can be essentially non-birefringent and even ambient), and while an input lens or output lens can be considered to be formed by a plurality of elements, (eg. two elements made of different materials such as Fused Silica and Calcium Fluoride), the step a. providing of spatially separated input and output lenses is best exemplified as being practiced by the providing of an ellipsometer system that has both input and output lenses present therein through which an beam of electromagnetic radiation is caused to convergently enter and exit in a recolliminated form, repectively.
Any method of the present invention can further involve, in a functional order the following steps a1.-a4:
a1. fixing evaluated parameter values in mathematical model parameterized equations, for each of said input lens and output lens, such that said parameterized equations allow independent determination of retardation entered between orthogonal components of a beam of electromagnetic radiation caused to pass through said input and output lenses, given wavelength; and
a2. causing an unknown material system to be present on said means for supporting a material system;
a3. obtaining a spectroscopic set of ellipsometric data with said unknown material system present on the means for supporting a material system, utilizing a beam of electromagnetic radiation provided by said source of electromagnetic radiation, said beam of electromagnetic radiation being caused to pass through said input lens, interact with said alternative material system in a plane of incidence thereto, and exit through said output lens and enter said detector system; and
a4. by utilizing said mathematical model for said input lens and said output lens in which parameter values in mathematical model parameterized equations, for each of said input lens and output lens have been fixed, simultaneously evaluating PSI""S and uncorrelated DELTA""S parameters for said unknown material system.
As in other steps in the present invention method in which parameter values are evaluated, it is again noted that the method of accurately evaluating parameters in parameterized equations in a mathematical model of a system of spatially separated input and output lenses in which said simultaneous evaluation of PSI""S and DELTA""S for said unknown material are typically achieved by a square error reducing mathematical curve fitting procedure.
As alluded to earlier, the step of providing spatially separated input and output lenses, at least one of said input and output lenses demonstrating birefringence when a beam of electromagnetic radiation is caused to pass therethrough, can involve one or both lens(es) which is/are not birefringent. And, said at least one lens which is not birefringent can be essentially a surrounding ambient, (ie. a phantom lens which is essentially just the atmosphere surrounding a material system).
It is noted that where parameters in parameterized equations for out-of-plane retardance equations have been determined, a focused version of the present invention method for accurately evaluating parameters in parameterized equations in a mathematical model of a system of spatially separated input and output lenses can comprise the steps of b1-b7:
b1. fixing evaluated parameter values in mathematical model parameterized equations, for each of said input lens and output lens, such that said parameterized equations allow independent determination of retardation entered between orthogonal components of a beam of electromagnetic radiation caused to pass through said input and output lenses, given wavelength; and
b2. causing an unknown material system to be present on said means for supporting a material system;
b3. obtaining a spectroscopic set of ellipsometric data with said unknown material system present on the means for supporting a material system, utilizing a beam of electromagnetic radiation provided by said source of electromagnetic radiation, said beam of electromagnetic radiation being caused to pass through said input lens, interact with said alternative material system in a plane of incidence thereto, and exit through said output lens and enter said detector system; and
b4. by utilizing said mathematical model for said input lens and said output lens in which parameter values in mathematical model parameterized equations, for each of said input lens and output lens have been fixed, simultaneously evaluating ALPHA""S and BETA""S for said unknown material system, (see the Detailed Description for definition of ALPHA""S and BETA""S);
b5. applying transfer functions to said simultaneously evaluated ALPHA""S and BETA""S for said unknown material system to the end that a data set of effective PSI""s and DELTA""s for a combination of said lenses and said material system is provided;
b6. providing a mathematical model for said combination of said lenses and said material system which separately accounts for the retardation effects of the presence of said lenses and said material system by parameterized equations; and
b7. by utilizing said mathematical model for said combination of said lenses and said material system which separately accounts for the effects of the presence of at least said lenses by parameterized equations; and said data set of effective PSI""s and DELTA""s for a combination of said lenses and said material system, simultaneously evaluating actual PSI""s and DELTA""s for said unknown material system per se.
In the case, for instance, where the ellipsometer involved is a Rotating Analyzer, or Rotating Polarizer ellipsometer system, (but not where the ellipsometer involved is a Rotating Compensator System), it is noted that determination of xe2x80x9cHandednessxe2x80x9d is required. Therefore the foregoing method can include, as necessary, providing a mathematical model for said combination of said lenses and said material system which separately accounts for the retardation effects of the presence of said lenses and said material system by parameterized equations which further includes providing for the effects of Handedness. It is specifically stated that where the present invention approach of regressing onto effective PSI and DELTA values, (as determined in step b7.), is utilized, the mathematical model can be derived so that xe2x80x9cHandednessxe2x80x9d is accounted for in arriving at actual PSI""s and DELTA""s for said unknown material system per se.
As a general comment it is to be understood that separate PSI and DELTA values are achieved for each angle of incidence a beam of electromagnetic radiation makes with respect to a material substrate and for each wavelength utilized in a spectroscopic range of wavelengths.
Also, as the present invention methodology finds application in ellipsometer systems in which are present input and/or output lenses, the foregoing methods of use are recited utilizing specific reference to input and output lenses in ellipsometer systems. In general said methodology can be applied where any input and/or output optical elements are present.
Finally, while the forgoing has presented method steps in a logical to enhance disclosure, it is to be understood that the steps of any method recitation in this Specification can be practiced in any functional order and remain within the scope of the present invntion.
The present invention will be better understood by reference to the Detailed Description Section of this Disclosure, with appropriate reference being has to the Drawings.
It is a primary objective and/or purpose of the present invention to describe a lens system which enables practice of focused beam small-spot spectroscopic ellipsometry over a large wavelength range, including into the deep UV, (eg. wavelengths down to and below 190 NM). Multi-element lenses which comrpise elements made of different materials allow essentially the same focal length to be achieved over a wide wavelength range.
It is another primary objective and/or purpose of the present invention to provide methods, (as originally presented in Parent application Ser. No. 09/162,217 as regards compensating Vacuum Window Birefringence), for essentially eliminating birefringence achromatic effects of multiple element input and output lenses, (optionally in combination with other ellipsometrically indistinguishable elements), in the analysis of ellipsometric data obtained utilizing an ellipsometer system beam of electromagnetic radiation which passes through said lenses.
Other objectives and/or purposes will become apparent by reference to other sections of this Specification.